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This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

Additive Manufacturing (AM) is already well-established for various manufacturing applications, providing many benefits such as design freedom, novel and complex cooling designs for the parts and different performance improvements, as well as significantly reducing the production time. With the mentioned characteristics, AM is also being considered as a technology for manufacturing a Radio Frequency Quadrupole (RFQ) prototype. For this application, an important parameter is the voltage holding capability of the surfaces. Furthermore, the voltage holding capability of pure copper surfaces manufactured by AM is of interest for the accelerator community at large for prospective future developments. To characterize these properties, a series of high electric field tests were performed on pure copper electrodes produced by AM, using the CERN pulsed high-voltage DC system. The tests were carried out with AM produced electrodes with large surface roughness. During the testing process, a high vacuum was maintained. The electric breakdown rate was also monitored to ensure not to exceed the breakdown limit of 10 $^{-5}$ breakdowns per pulse. The achieved results provide the first, initial reference values for the performance of AM built pure copper electrodes for vacuum arc breakdown testing. Initial results prove the capability of AM electrodes to hold a high electric field, while having low breakdown rates. These are crucial results for further AM technology usage for different AM pure-copper accelerator components, Comment: Inproceedings IPAC2023, JACoW Publishing, ISBN: 978-3-95450-231-8

Particle accelerators with superconducting magnets operating at cryogenic temperatures use a beam screen (BS) liner that extracts heat generated by the circulating bunched charge particle beam before it can reach the magnets. The BS surface, commonly made of high-conductivity copper, provides a low impedance for beam stability reasons, low secondary electron yield (SEY)to mitigate the electron-cloud (EC) effect, and low electron-stimulated desorption yield (ESD) to limit the dynamic pressure rise due to EC. Rare-earth barium copper oxide (REBCO) high-temperature superconductors (HTs) recently reached technical maturity, are produced as coated conductor tapes (REBCO-CCs), and will be considered for application in future colliders to decrease the BS impedance and enable operation at around 50 K, consequently relaxing the cryogenic requirements. Aside from HTS properties, industry-grade REBCO-CCs also need qualification for EC and dynamic vacuum compatibility under accelerator-like conditions. Hence, we report the SEY and ESD measured at cryogenic temperatures of 12 K under low-energy electron irradiation of 0 - 1.4 keV. We also verify the sample compositions and morphologies using XPS, SEM, and EDS methods. The energy and dose dependencies of ESD are comparable to those of technical-grade metals and one sample reached SEY$_{MAX}=$1.2 after electron conditioning.

During operation, the radio-frequency quadrupole (RFQ) of the LINAC4 at CERN is exposed to high electric fields, which can lead to vacuum breakdown. It is also subject to beam loss, which can cause surface modification, including blistering, which can result in reduced electric field holding and an increased breakdown rate. First, experiments to study the high-voltage conditioning process and electrical breakdown statistics have been conducted using pulsed high voltage DC systems in order to identify materials with high electric field handling capability and robustness to low-energy irradiation. In this paper, we discuss the results obtained for the different materials tested. To complement these, an investigation of their metallurgical properties using advanced microscopic techniques was done to observe and characterize the different materials and to compare results before and after irradiation and breakdown testing.

This work studies the suitability of a set of different materials for manufacturing of more efficient and durable Radio-Frequency Quadrupole (RFQ) structures compared to that currently used in many linear particle accelerators, traditionally made out of copper. RFQs are susceptible to vacuum breakdowns caused by the exposure to high electric fields, resulting in surface degradation. Additionally, a further limitation of present-day copper RFQs is surface blistering under hydrogen ion beam exposure, due to beam halo losses. Irradiation is associated with a further reduction of the breakdown field strength of the metal surface thereby affecting the overall efficiency of the RFQ. The investigated materials, Cu-OFE, CuCr1Zr, CuBe2, Ti6Al4V, SS316LN, Nb and Ta, were submitted to low-energy (45 keV) H$^-$ irradiation and tested in a direct-current (DC) system with pulsed high voltage. For comparison, the maximum surface electric field was measured for both irradiated and pristine (non irradiated) surfaces of the same material. The effects of irradiation on the surface of the materials, before and after being submitted to high electric fields, were studied with the help of microscopic imaging and chemical analysis. Blistering caused by H$^-$ irradiation has been observed in all copper and copper alloy materials. Despite reductions in breakdown field strength post-irradiation, no indications were found that the blisters on the surface have a direct cause in triggering breakdowns during high electric field tests. SS316LN, Ti6Al4V, CuBe2 and CuCr1Zr showed maximum surface electric fields higher than copper, making these promising candidate materials for future RFQs manufacturing. This paper focuses on the results with CuCr1Zr, CuBe2, SS316LN and Ta, complementing and expanding previous work exploring Cu-OFE, Nb and Ti6Al4V.

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider., Comment: This document summarises the International Muon Collider Collaboration (IMCC) progress and status of the Muon Collider R&D programme

Off-the-grid regularisation has been extensively employed over the last decade in the context of ill-posed inverse problems formulated in the continuous setting of the space of Radon measures $\mathcal{M}(\mathcal{X})$. These approaches enjoy convexity and counteract the discretisation biases as well the numerical instabilities typical of their discrete counterparts. In the framework of sparse reconstruction of discrete point measures (sum of weighted Diracs), a Total Variation regularisation norm in $\mathcal{M}(\mathcal{X})$ is typically combined with an $L^2$ data term modelling additive Gaussian noise. To asses the framework of off-the-grid regularisation in the presence of signal-dependent Poisson noise, we consider in this work a variational model coupling the Total Variation regularisation with a Kullback-Leibler data term under a non-negativity constraint. Analytically, we study the optimality conditions of the composite functional and analyse its dual problem. Then, we consider an homotopy strategy to select an optimal regularisation parameter and use it within a Sliding Frank-Wolfe algorithm. Several numerical experiments on both 1D/2D simulated and real 3D fluorescent microscopy data are reported.

We propose an unfolded accelerated projected-gradient descent procedure to estimate model and algorithmic parameters for image super-resolution and molecule localization problems in image microscopy. The variational lower-level constraint enforces sparsity of the solution and encodes different noise statistics (Gaussian, Poisson), while the upper-level cost assesses optimality w.r.t.~the task considered. In more detail, a standard $\ell_2$ cost is considered for image reconstruction (e.g., deconvolution/super-resolution, semi-blind deconvolution) problems, while a smoothed $\ell_1$ is employed to assess localization precision in some exemplary fluorescence microscopy problems exploiting single-molecule activation. Several numerical experiments are reported to validate the proposed approach on synthetic and realistic ISBI data.

We describe the results of a haloscope axion search performed with an 11.7 T dipole magnet at CERN. The search used a custom-made radio-frequency cavity coated with high-temperature superconducting tape. A set of 27 h of data at a resonant frequency of around 8.84 GHz was analysed. In the range of axion mass 36.5676 $\mu$eV to 36.5699 $\mu$eV, corresponding to a width of 554 kHz, no signal excess hinting at an axion-like particle was found. Correspondingly, in this mass range, a limit on the axion to photon coupling-strength was set in the range between g$_{a\gamma}\gtrsim$ 6.2e-13 GeV$^{-1}$ and g$_{a\gamma}\gtrsim$ 1.54e-13 GeV$^{-1}$ with a 95% confidence level., Comment: 19 pages, 8 figures

We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics relying either on the prior knowledge of reference data and/or on some (partial) knowledge on the noise statistics, the proposed approach optimizes the whiteness of the residual between the observed data and the observation model with no need of ground-truth data.We validate the approach on standard Total Variation-regularized image deconvolution problems which show that the proposed quality metric provides estimates close to the mean-square error oracle and to discrepancy-based principles.

In order to investigate the dependence of conditioning and field-holding on temperature, three pairs of copper electrodes underwent high voltage conditioning with direct current (DC) pulses while kept at a single temperature, unique for each set (300~K, 30~K and 10~K), until saturation field for each set was found. The sets conditioned at cold showed a significant increase in the field holding capability, reaching fields up to 147 MV/m after tens of millions of pulses and very few breakdowns (BDs). We interpret this as an indication of the conditioning effect being due to high field pulsing rather than exposure to BDs. The effect of the warm and cold conditioning was investigated with high-resolution microscopy, characterizing the BD spots on the anode and cathode according to their morphology and with scanning transmission electron microscopy (STEM) analyzing the changes in the sub-surface regions. Atypical BD spot features were found on the cryogenically conditioned cathode surfaces, with very shallow craters of a star-like shape. The number of atypical spots increased with decreased temperatures, reaching 26 and 53 percent of the total number of spots at 30~K and 10~K, respectively. A hypothesis explaining the formation of these features is also presented. The very different morphology of the anode and cathode BD spots is presented in detail that suggesting an unknown shielding mechanism that prevents the center of the anode spot from melting. These results provide important experimental input for the development of quantitative theories and models for BD initiation and inter-electrode plasma formation.

We propose a new class of exact continuous relaxations of l0-regularized criteria involving non-quadratic data terms such as the Kullback-Leibler divergence and the logistic regression, possibly combined with an l2 regularization. We first prove the existence of global minimizers for such problems and characterize their local minimizers.Then, we propose the l0 Bregman Relaxation (B-rex), a continuous approximation of the l0 pseudo-norm defined in terms of suitable Bregman distances, which leads to an exact continuous relaxations of the original l0-regularized problem in the sense that it does not alter its set of global minimizers and reduces the non-convexity by eliminating certain local minimizers. Both features make the relaxed problem more amenable to be solved by standard non-convex optimization algorithms. In this spirit, we consider the proximal gradient algorithm and provide explicit computation of proximal points for the B-rex penalty in several cases. Finally, we report a set of numerical results illustrating the geometrical behavior of the proposed B-rex penalty for different choices of the underlying Bregman distance, its relation with convex envelopes, as well as its exact relaxation properties in 1D/2D and higher dimensions.

The axion haloscope is the currently most sensitive method to probe the vanishingly small coupling of this prominent Dark Matter candidate to photons. To scan a sizeable axion Dark Matter parameter space, the cavities that make up the haloscope need to be tuned efficiently. In this article, we describe a novel technique to tune axion haloscopes around $8.4$ GHz in a purely mechanical manner without the use of dielectrics. We achieve tuning by introducing a gap along the cavity geometry. Losses are added due to the leaking of the field out of the structure only if the gap becomes too large concerning the total width. A tuning range of around $600$ MHz is achieved, depending on the environmental conditions. We present the results of a corresponding prototype and outline prospects to further develop this technique.

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

We consider a combined restarting and adaptive backtracking strategy for the popular Fast Iterative Shrinking-Thresholding Algorithm frequently employed for accelerating the convergence speed of large-scale structured convex optimization problems. Several variants of FISTA enjoy a provable linear convergence rate for the function values $F(x_n)$ of the form $\mathcal{O}( e^{-K\sqrt{\mu/L}~n})$ under the prior knowledge of problem conditioning, i.e. of the ratio between the (\L ojasiewicz) parameter $\mu$ determining the growth of the objective function and the Lipschitz constant $L$ of its smooth component. These parameters are nonetheless hard to estimate in many practical cases. Recent works address the problem by estimating either parameter via suitable adaptive strategies. In our work both parameters can be estimated at the same time by means of an algorithmic restarting scheme where, at each restart, a non-monotone estimation of $L$ is performed. For this scheme, theoretical convergence results are proved, showing that a $\mathcal{O}( e^{-K\sqrt{\mu/L}n})$ convergence speed can still be achieved along with quantitative estimates of the conditioning. The resulting Free-FISTA algorithm is therefore parameter-free. Several numerical results are reported to confirm the practical interest of its use in many exemplar problems.

In the near future BabyIAXO will be the most powerful axion helioscope, relying on a custom-made magnet of two bores of 70 cm diameter and 10 m long, with a total available magnetic volume of more than 7 m$^3$. In this document, we propose and describe the implementation of low-frequency axion haloscope setups suitable for operation inside the BabyIAXO magnet. The RADES proposal has a potential sensitivity to the axion-photon coupling $g_{a\gamma}$ down to values corresponding to the KSVZ model, in the (currently unexplored) mass range between 1 and 2$~\mu$eV, after a total effective exposure of 440 days. This mass range is covered by the use of four differently dimensioned 5-meter-long cavities, equipped with a tuning mechanism based on inner turning plates. A setup like the one proposed would also allow an exploration of the same mass range for hidden photons coupled to photons. An additional complementary apparatus is proposed using LC circuits and exploring the low energy range ($\sim10^{-4}-10^{-1}~\mu$eV). The setup includes a cryostat and cooling system to cool down the BabyIAXO bore down to about 5 K, as well as appropriate low-noise signal amplification and detection chain.

A novel numerical strategy is introduced for computing approximations of solutions to a Cahn-Hilliard model with degenerate mobilities. This model has recently been introduced as a second-order phase-field approximation for surface diffusion flows. Its numerical discretization is challenging due to the degeneracy of the mobilities, which generally requires an implicit treatment to avoid stability issues at the price of increased complexity costs. To mitigate this drawback, we consider new first- and second-order Scalar Auxiliary Variable (SAV) schemes that, differently from existing approaches, focus on the relaxation of the mobility, rather than the Cahn-Hilliard energy. These schemes are introduced and analysed theoretically in the general context of gradient flows and then specialised for the Cahn-Hilliard equation with mobilities. Various numerical experiments are conducted to highlight the advantages of these new schemes in terms of accuracy, effectiveness and computational cost., Comment: 27 pages, 10 figures

The unprecedented success of image reconstruction approaches based on deep neural networks has revolutionised both the processing and the analysis paradigms in several applied disciplines. In the field of digital humanities, the task of digital reconstruction of ancient frescoes is particularly challenging due to the scarce amount of available training data caused by ageing, wear, tear and retouching over time. To overcome these difficulties, we consider the Deep Image Prior (DIP) inpainting approach which computes appropriate reconstructions by relying on the progressive updating of an untrained convolutional neural network so as to match the reliable piece of information in the image at hand while promoting regularisation elsewhere. In comparison with state-of-the-art approaches (based on variational/PDEs and patch-based methods), DIP-based inpainting reduces artefacts and better adapts to contextual/non-local information, thus providing a valuable and effective tool for art historians. As a case study, we apply such approach to reconstruct missing image contents in a dataset of highly damaged digital images of medieval paintings located into several chapels in the Mediterranean Alpine Arc and provide a detailed description on how visible and invisible (e.g., infrared) information can be integrated for identifying and reconstructing damaged image regions., Comment: 26 pages

We present results from exploratory studies, supported by the Physics Beyond Colliders (PBC) Study Group, of the suitability of a CERN site and its infrastructure for hosting a vertical atom interferometer (AI) with a baseline of about 100 m. We first review the scientific motivations for such an experiment to search for ultralight dark matter and measure gravitational waves, and then outline the general technical requirements for such an atom interferometer, using the AION-100 project as an example. We present a possible CERN site in the PX46 access shaft to the Large Hadron Collider (LHC), including the motivations for this choice and a description of its infrastructure. We then assess its compliance with the technical requirements of such an experiment and what upgrades may be needed. We analyse issues related to the proximity of the LHC machine and its ancillary hardware and present a preliminary safety analysis and the required mitigation measures and infrastructure modifications. In conclusion, we identify primary cost drivers and describe constraints on the experimental installation and operation schedules arising from LHC operation. We find no technical obstacles: the CERN site is a very promising location for an AI experiment with a vertical baseline of about 100 m., Comment: 51 pages, 39 figures, version with higher resolution figures available from https://cds.cern.ch/record/2851946/

The spatial resolution of images of living samples obtained by fluorescence microscopes is physically limited due to the diffraction of visible light, which makes the study of entities of size less than the diffraction barrier (around 200 nm in the x-y plane) very challenging. To overcome this limitation, several deconvolution and super-resolution techniques have been proposed. Within the framework of inverse problems, modern approaches in fluorescence microscopy reconstruct a super-resolved image from a temporal stack of frames by carefully designing suitable hand-crafted sparsity-promoting regularisers. Numerically, such approaches are solved by proximal gradient-based iterative schemes. Aiming at obtaining a reconstruction more adapted to sample geometries (e.g. thin filaments), we adopt a plug-and-play denoising approach with convergence guarantees and replace the proximity operator associated with the explicit image regulariser with an image denoiser (i.e. a pre-trained network) which, upon appropriate training, mimics the action of an implicit prior. To account for the independence of the fluctuations between molecules, the model relies on second-order statistics. The denoiser is then trained on covariance images coming from data representing sequences of fluctuating fluorescent molecules with filament structure. The method is evaluated on both simulated and real fluorescence microscopy images, showing its ability to correctly reconstruct filament structures with high values of peak signal-to-noise ratio (PSNR).

We consider a stochastic gradient descent (SGD) algorithm for solving linear inverse problems (e.g., CT image reconstruction) in the Banach space framework of variable exponent Lebesgue spaces $\ell^{(p_n)}(\mathbb{R})$. Such non-standard spaces have been recently proved to be the appropriate functional framework to enforce pixel-adaptive regularisation in signal and image processing applications. Compared to its use in Hilbert settings, however, the application of SGD in the Banach setting of $\ell^{(p_n)}(\mathbb{R})$ is not straightforward, due, in particular to the lack of a closed-form expression and the non-separability property of the underlying norm. In this manuscript, we show that SGD iterations can effectively be performed using the associated modular function. Numerical validation on both simulated and real CT data show significant improvements in comparison to SGD solutions both in Hilbert and other Banach settings, in particular when non-Gaussian or mixed noise is observed in the data., Comment: 13 pages, 3 figures, submitted to SSVM2023

Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired quantities of interest (e.g., regularization terms or discretization filters), such approach computes optimal parameter values by solving a nested optimization problem where the variational model acts as a constraint. In this work, we consider two different use cases of bilevel learning for the problem of image restoration. First, we focus on learning scalar weights and convolutional filters defining a Field of Experts regularizer to restore natural images degraded by blur and noise. For improving the practical performance, the lower-level problem is solved by means of a gradient descent scheme combined with a line-search strategy based on the Barzilai-Borwein rule. As a second application, the bilevel setup is employed for learning a discretization of the popular total variation regularizer for solving image restoration problems (in particular, deblurring and super-resolution). Numerical results show the effectiveness of the approach and their generalization to multiple tasks., Comment: Acknowledgments corrected

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the $\ell_1$ norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the $\ell_1$ norm is highly suboptimal compared to other functions suited to approximating $\ell_q$ with $0 \leq q < 1 $ (including recently proposed Continuous Exact relaxations), both in terms of performance and in the production of features that are akin to signatures of the primary visual cortex. We show that $\ell_1$ sparsity produces a denser code or employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. For all the penalty functions tested, a subset of the neurons develop orientation selectivity similarly to V1 neurons. When their code is sparse enough, the methods also develop receptive fields with varying functionalities, another signature of V1. Compared to other methods, soft thresholding achieves this level of sparsity at the expense of much degraded reconstruction performance, that more likely than not is not acceptable in biological vision. Our results indicate that V1 uses a sparsity inducing regularization that is closer to the $\ell_0$ pseudo-norm rather than to the $\ell_1$ norm.

When metal surfaces are exposed to hydrogen ion irradiation, the light ions are expected to penetrate deep into the material and dissolve in the matrix. However, these atoms are seen to cause significant modification of surfaces, indicating that they accumulate in vicinity of the surface. The process known as blistering may reduces the vacuum dielectric strength above the metal surface, which shows a dense population of surface blisters. In this paper, we investigate how a bubble can grow under the pressure exerted by hydrogen atoms on the walls of the bubble and how this affect to the surface of Cu, whether an external electric field is applied or not.

We consider a non-linear variant of the transport-diffusion osmosis model for solving a variety of imaging problems such as shadow/soft-light removal and compact data representation. The non-linear behaviour is encoded in terms of a general scalar function g with suitable properties, which allows to balance the diffusion intensity on the different regions of the image while preventing smoothing artefacts. For the proposed model, conservation properties (intensity and non-negativity) are proved and a variational interpretation is showed for specific choices of g. Upon suitable spatial discretisation, both an explicit and a semi-implicit iterative scheme are considered, for which convergence restrictions and unconditional stability are proved, respectively. To validate the proposed modelling and the computational speed of the numerical schemes considered, we report several results and comparisons for the problem of shadow/light-spot removal and compact data representation, showing that artefact-free and computationally efficient results are obtained in comparison to standard linear and anisotropic models, and state-of-the art approaches., Comment: 25 pages, 14 figures

The Compact Linear Collider (CLIC) is a multi-TeV high-luminosity linear e$^+$e$^-$-collider under development by the CLIC accelerator collaboration, hosted by CERN. The CLIC accelerator has been optimised for three energy stages at centre-of-mass energies 380 GeV, 1.5 TeV and 3 TeV. CLIC uses a novel two-beam acceleration technique, with normal-conducting accelerating structures operating in the range of 70-100 MV/m. The report describes recent achievements in accelerator design, technology development and prototyping, system tests and beam tests. Large-scale CLIC-specific beam tests have taken place, for example, at the CLIC Test Facility CTF3 at CERN, at the Accelerator Test Facility ATF2 at KEK, at the FACET facility at SLAC and at the FERMI facility in Trieste. Together, they demonstrate that all implications of the CLIC design parameters are well understood and reproducible in beam tests and prove that the CLIC performance goals are realistic. The implementation of CLIC near CERN has been investigated. Focusing on a staged approach starting at 380 GeV, this includes civil engineering aspects, electrical networks, cooling and ventilation and installation scheduling, transport. All CLIC studies have put emphasis on optimising cost and energy efficiency, and the resulting power and cost estimates are reported. The report follows very closely the accelerator project description in the CLIC Summary Report for the European Particle Physics Strategy update 2018-19. Detailed studies of the physics potential and detector for CLIC, and R&D on detector technologies, have been carried out by the CLIC detector and physics (CLICdp) collaboration. CLIC provides excellent sensitivity to Beyond Standard Model physics, through direct searches and via a broad set of precision measurements of Standard Model processes, particularly in the Higgs and top-quark sectors., Comment: arXiv admin note: substantial text overlap with arXiv:1812.06018, arXiv:1903.08655

The 2020 update of the European Strategy for Particle Physics emphasised the importance of an intensified and well-coordinated programme of accelerator R&D, supporting the design and delivery of future particle accelerators in a timely, affordable and sustainable way. This report sets out a roadmap for European accelerator R&D for the next five to ten years, covering five topical areas identified in the Strategy update. The R&D objectives include: improvement of the performance and cost-performance of magnet and radio-frequency acceleration systems; investigations of the potential of laser / plasma acceleration and energy-recovery linac techniques; and development of new concepts for muon beams and muon colliders. The goal of the roadmap is to document the collective view of the field on the next steps for the R&D programme, and to provide the evidence base to support subsequent decisions on prioritisation, resourcing and implementation., Comment: 270 pages, 58 figures. Editor: N. Mounet. LDG chair: D. Newbold. Panel chairs: P. V\'edrine (HFM), S. Bousson (RF), R. Assmann (plasma), D. Schulte (muon), M. Klein (ERL). Panel editors: B. Baudouy (HFM), L. Bottura (HFM), S. Bousson (RF), G. Burt (RF), R. Assmann (plasma), E. Gschwendtner (plasma), R. Ischebeck (plasma), C. Rogers (muon), D. Schulte (muon), M. Klein (ERL)

We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to their intrinsic space-variant properties, such spaces can be naturally used as solution space and combined with space-variant functionals for the solution of ill-posed inverse problems. For this purpose, we propose and analyse two instances (primal and dual) of proximal gradient algorithms in $L_{p(\cdot)}(\Omega)$, where the proximal step, rather than depending on the natural (non-separable) $L_{p(\cdot)}(\Omega)$ norm, is defined in terms of its modular function, which, thanks to its separability, allows for the efficient computation of algorithmic iterates. Convergence in function values is proved for both algorithms, with convergence rates depending on problem/space smoothness. To show the effectiveness of the proposed modelling, some numerical tests highlighting the flexibility of the space $L_{p(\cdot)}(\Omega)$ are shown for exemplar deconvolution and mixed noise removal problems. Finally, a numerical verification on the convergence speed and computational costs of both algorithms in comparison with analogous ones defined in standard $L_{p}(\Omega)$ spaces is presented.

Within the increasing interest in the dark matter axion detection through haloscopes, in which different international groups are currently involved, the RADES group was established in 2016 with the goal of developing very sensitive detection systems to be operated in dipole magnets. This review deals with the work developed by this collaboration during its first five years, from the first designs, based on the multi-cavity concept, aiming to increase the haloscope volume and, so, to improve its sensitivity, their evolution, the data acquisition design, and, finally, the first experimental run. Moreover, the envisaged work within RADES, for both dipole and solenoid magnets, in the short and medium term is also presented., Comment: Review paper, 24 pages, 18 figures, 57 references

We propose a 3D super-resolution approach to improve both lateral and axial spatial resolution in Total Internal Reflectance Fluorescence (TIRF) imaging applications. Our approach, called 3D-COL0RME (3D - Covariance-based $\ell_0$ super-Resolution Microscopy with intensity Estimation) improves both lateral and axial resolution by combining sparsity-based modelling for precise molecule localisation and intensity estimation in the lateral plane with a 3D reconstruction procedure in the axial one using Multi-Angle TIRF (MA-TIRF). Differently from state-of-the-art approaches, 3D-COL0RME does not require the use of special equipment as it can be used with standard fluorophores. We validate 3D-COL0RME on simulated MA-TIRF blinking-type data and on challenging real MA-TIRF acquisitions, showing significant resolution improvements., Comment: Published in 2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI)

The axion is a hypothetical particle which is a candidate for cold dark matter. Haloscope experiments directly search for these particles in strong magnetic fields with RF cavities as detectors. The Relic Axion Detector Exploratory Setup (RADES) at CERN in particular is searching for axion dark matter in a mass range above 30 $\mu$eV. The figure of merit of our detector depends linearly on the quality factor of the cavity and therefore we are researching the possibility of coating our cavities with different superconducting materials to increase the quality factor. Since the experiment operates in strong magnetic fields of 11 T and more, superconductors with high critical magnetic fields are necessary. Suitable materials for this application are for example REBa$_2$Cu$_3$O$_{7-x}$, Nb$_3$Sn or NbN. We designed a microwave cavity which resonates at around 9~GHz, with a geometry optimized to facilitate superconducting coating and designed to fit in the bore of available high-field accelerator magnets at CERN. Several prototypes of this cavity were coated with different superconducting materials, employing different coating techniques. These prototypes were characterized in strong magnetic fields at 4.2 K., Comment: 5 pages, 6 figures. v2: minor updates after referee comments, matches published version in IEEE